Re: A Guide for Cantor Cranks

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Article #801

#801

From: Virgil
Date: Mon, 21 Mar 2011 21:12

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In article 
<9c851574-eb70-45c4-b6e3-9351a7679223@k30g2000yqb.googlegroups.com>,
 William Hughes <wpihughes@gmail.com> wrote:

> On Mar 21, 3:33�am, Graham Cooper <grahamcoop...@gmail.com> wrote:
> > On Mar 21, 2:30�pm, William Hughes <wpihug...@gmail.com> wrote:
> >
> > > > My point is you can't support your claim with 2 given diagonals.
> >
> > > My claim is that given a list of binary sequences I can find a
> > > sequence
> > > not on the list.
> >
> > > To support this claim I need only one diagonal. �When you gave me
> > > two diagonals I chose one and supported the claim.
> >
> > > Your claim that you can get a generalized diagonal with any finite
> > > prefix is true, but irrelevant. �You cannot set the generalized
> > > diagonal to an arbitrary sequence.
> > > � � � � � � � � � � � � � � � � � � �- William Hughes
> >
> > You haven't proven your sequence is not on the list in the 2 diagonal
> > version.
> >
> > AD1 = 1110...
> > AD2 = 0110...
> >
> > Can you prove EITHER real is missing from my (secret) list given only
> > the above?
> >
> > IF YES, then by all means do so!
> 
> There is a sequence not on your secret list that starts
> 1100.  Proof: the n'th digit means that sequence is not
> the n'th line of the list.  There may be other sequences that
> starts 1110 on your secret list.
>                                  -William Hughes

One can have a sequence not in a given list which stars with any fixed 
finite sequence of, say, k, positions, by having it differ from the nth 
sequence at position n + k.

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<40e69d0c-eb77-4308-996e-c7dfc1a0ec1e@j13g2000pro.googlegroups.com> <8b844723-fc35-410b-b05c-dc4799ed1c35@f2g2000yqf.googlegroups.com> <d3c279c6-b0d0-4da0-9360-d0c7a91980fb@n2g2000prj.googlegroups.com> <adc08cec-9301-4754-9fcf-61ffc38b5b74@s18g2000vbe.googlegroups.com> <ad7ef639-a0c7-4421-a8ca-1f121439228d@b4g2000vby.googlegroups.com> <9268ac3b-e542-412c-8927-a2fe082e6fb0@f31g2000pri.googlegroups.com> <07a61ecc-e3fd-4304-9977-f4f2724ef652@w21g2000yqm.googlegroups.com> <83c8a047-2cc6-4ed2-a74f-8329656c4f9f@j35g2000prb.googlegroups.com> <2d9a4e44-18dc-43fd-bec1-056b7b4ba26d@x11g2000yqc.googlegroups.com> <2298d465-e708-4801-be12-12c714cd98dc@f36g2000pri.googlegroups.com> <2e445897-6fc0-488d-9ab5-fcd1c7dc703d@f30g2000yqa.googlegroups.com> <efc21f2f-acb7-475d-87ab-fbfa35208c4c@o15g2000prn.googlegroups.com> <9c851574-eb70-45c4-b6e3-9351a7679223@k30g2000yqb.googlegroups.com>

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From: Virgil <Vir@gil.Gil>
Newsgroups: sci.logic,sci.math,comp.theory,sci.physics,aus.science
Subject: Re: A Guide for Cantor Cranks
Organization: Ligriv
References: <40e69d0c-eb77-4308-996e-c7dfc1a0ec1e@j13g2000pro.googlegroups.com> <8b844723-fc35-410b-b05c-dc4799ed1c35@f2g2000yqf.googlegroups.com> <d3c279c6-b0d0-4da0-9360-d0c7a91980fb@n2g2000prj.googlegroups.com> <adc08cec-9301-4754-9fcf-61ffc38b5b74@s18g2000vbe.googlegroups.com> <ad7ef639-a0c7-4421-a8ca-1f121439228d@b4g2000vby.googlegroups.com> <9268ac3b-e542-412c-8927-a2fe082e6fb0@f31g2000pri.googlegroups.com> <07a61ecc-e3fd-4304-9977-f4f2724ef652@w21g2000yqm.googlegroups.com> <83c8a047-2cc6-4ed2-a74f-8329656c4f9f@j35g2000prb.googlegroups.com> <2d9a4e44-18dc-43fd-bec1-056b7b4ba26d@x11g2000yqc.googlegroups.com> <2298d465-e708-4801-be12-12c714cd98dc@f36g2000pri.googlegroups.com> <2e445897-6fc0-488d-9ab5-fcd1c7dc703d@f30g2000yqa.googlegroups.com> <efc21f2f-acb7-475d-87ab-fbfa35208c4c@o15g2000prn.googlegroups.com> <9c851574-eb70-45c4-b6e3-9351a7679223@k30g2000yqb.googlegroups.com>
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